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Block #286,142

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/30/2013, 6:52:10 PM Β· Difficulty 9.9852 Β· 6,510,760 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
6bdd26f6092a44edfec07cea2ee5f08574eca3e868c7bbea0072a34ab0c6558c
View on Chainz β†—

Height

#286,142

Difficulty

9.985203

Transactions

3

Size

764 B

Version

2

Bits

09fc3649

Nonce

12,318

Timestamp

11/30/2013, 6:52:10 PM

Confirmations

6,510,760

Mined by

⛏️ P2SHAUMMTB5NwPQNvJxTvLVYWyEYFskEjbv3x6

Merkle Root

5386aa005295dbb0729be8d37e11697f004714e207c677310dd36e9633ffff51
Transactions (3)
Coinbase3ffe5b5ca63303…df65ee9c0213ba
1 in β†’ 1 out10.0300 XPM109 B
AUMMTB5N…kEjbv3x6
3aab6751ea9e5f…14d24e39c64227
2 in β†’ 1 out10.2000 XPM339 B
AR7hcJ3o…Yricu7HP
bb3590506efcf2…9e7fa458918688
1 in β†’ 2 out2.9631 XPM226 B
AbrYCoAS…jQet48pwASdk6JLt…F5AtD55r
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.466 Γ— 10⁹⁴(95-digit number)
44668129014823580254…81476297838305158899
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
4.466 Γ— 10⁹⁴(95-digit number)
44668129014823580254…81476297838305158899
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.466 Γ— 10⁹⁴(95-digit number)
44668129014823580254…81476297838305158901
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
8.933 Γ— 10⁹⁴(95-digit number)
89336258029647160509…62952595676610317799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.933 Γ— 10⁹⁴(95-digit number)
89336258029647160509…62952595676610317801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.786 Γ— 10⁹⁡(96-digit number)
17867251605929432101…25905191353220635599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.786 Γ— 10⁹⁡(96-digit number)
17867251605929432101…25905191353220635601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
3.573 Γ— 10⁹⁡(96-digit number)
35734503211858864203…51810382706441271199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.573 Γ— 10⁹⁡(96-digit number)
35734503211858864203…51810382706441271201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
7.146 Γ— 10⁹⁡(96-digit number)
71469006423717728407…03620765412882542399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.146 Γ— 10⁹⁡(96-digit number)
71469006423717728407…03620765412882542401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,619,237 XPMΒ·at block #6,796,901 Β· updates every 60s
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